Abstract
A submanifold of Rn whose tangent space makes constant angle with a fixed direction d is called a helix. Helix submanifolds are related with the eikonal PDE equation. We give a method to find every solution to the eikonal PDE on a Riemannian manifold locally. As a consequence we give a local construction of arbitrary Euclidean helix submanifolds of any dimension and codimension. Also we characterize the ruled helix submanifolds and in particular we describe those which are minimal.
Citation
Antonio J. Di Scala. Gabriel Ruiz-Hernández. "Higher codimensional Euclidean helix submanifolds." Kodai Math. J. 33 (2) 192 - 210, June 2010. https://doi.org/10.2996/kmj/1278076336
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